Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#4034 | C2 | semidirect |
| 3. C3×C5×#107 | C2 | semidirect |
| 5. C3×#3946 | C2 | semidirect |
| 7. C3×#3939 | C2 | semidirect |
| 8. #65179 | C3 | direct (N × H) |
| 22. #4034 | C2×C3 | semidirect |
| 23. C5×#107 | C2×C3 | semidirect |
| 25. #3946 | C2×C3 | semidirect |
| 27. #3939 | C2×C3 | semidirect |
| 36. C3×D20 | Q8 | semidirect |
| 44. C3×#107 | D5 | semidirect |
| 90. D20 | C3×Q8 | semidirect |
| 98. #107 | C3×D5 | semidirect |
| 141. C3×C5 | #474 | semidirect |
| 174. C5 | C3×#474 | semidirect |
| 186. C3 | #65179 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4039 | 2 |
| C3×#4034 | 2 |
| C3×C5×#107 | 2 |
| C3×#3953 | 2 |
| C3×#3946 | 2 |
| C3×#3941 | 2 |
| C3×#3939 | 2 |
| #65179 | 3 |
| C3×#474 | 5 |